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MHT CET202313 May 2023Evening ShiftMathematicsApplication of DerivativesActual

Slope of the tangent to the curve y=2 e ^x ( 4 - x 2 ) ( 4 - x 2 ) where 0 x 2 is minimum at x=

Options

  1. A0
  2. B2
  3. C1

Correct answer

B. 2

Step-by-step solution

y=2 e ^x ( 4 - x 2 ) ( 4 - x 2 ) aligned & = e ^x ( 2 -x ) [2 = 2 ] & = e ^x x aligned d y ~d x = e ^x( x- x) Let T = e ^x( x- x) dT d x = e ^x( x- x)+ e ^x(- x- x)=-2 e ^x x Now, dT d x =0 aligned & -2 e ^x x=0 & x=0 aligned x=0, , 2 [ 0 x 2 ] At x=0, ~T = e ^0( 0- 0)=1 At x= , T = e ^ ( - )=- e ^ At x=2 , T = e ^ 2 ( 2 - 2 )= e ^ 2 Slope of the tangent is minimum at x=

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